论文标题
系统耦合kuramoto-sivashinsky-kdv和椭圆方程的局部无效控制性
Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations
论文作者
论文摘要
本文在任何给定的时间$ t> 0 $的{\ em混合抛物线 - 纤维素elliptic pdes}系统的无效控制性。更准确地说，我们考虑\ textIt {kuramoto-sivashinsky-korteweg-de vries方程}，并与以间隔$（0,1）$相同的二阶椭圆方程式和二阶椭圆方程。我们首先表明线性化系统通过作用于KS-KDV或椭圆方程的局部内部控制，在全球范围内控制。使用\ textIt {Carleman方法}，我们提供了一个控件的存在，其显式成本$ ce^{c/t} $，其中一些常数$ c> 0 $独立于$ t $。然后，应用源术语方法，然后是\ textIt {Banach固定点定理}，我们结论了非线性系统的小型局部null可控性结果。
This paper deals with the null-controllability of a system of {\em mixed parabolic-elliptic pdes} at any given time $T>0$. More precisely, we consider the \textit{Kuramoto-Sivashinsky--Korteweg-de Vries equation} coupled with a second order elliptic equation posed in the interval $(0,1)$. We first show that the linearized system is globally null-controllable by means of a localized interior control acting on either the KS-KdV or the elliptic equation. Using the \textit{Carleman approach}, we provide the existence of a control with the explicit cost $Ce^{C/T}$ with some constant $C>0$ independent in $T$. Then, applying the source term method followed by the \textit{Banach fixed point theorem}, we conclude the small-time local null-controllability result of the nonlinear systems.
